A New Well-posed Nonlocal Perona-Malik Type Equation

Details A New Well-posed Nonlocal Perona-Malik Type Equation A New Well-posed Nonlocal Perona-Malik Type Equation

2007-02-23

arxiv.org/abs/math/0702715v1

Mathematics

Analysis of PDEs

Scientific paper

A modification of the Perona-Malik equation is proposed for which the local nonlinear diffusion term is replaced by a nonlocal term of slightly reduced ``strength''. The new equation is globally well-posed (in spaces of classical regularity) and possesses desirable properties from the perspective of image processing. It admits characteristic functions as (formally linearly ``stable'') stationary solutions and can therefore be reliably employed for denoising keeping blurring in check. Its numerical implementation is stable, enhances some of the features of Perona-Malik, and avoids problems known to affect the latter.

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